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Solving a Quadratic Equation by Completion of Squares Method

Solve the fol...

Question

Solve the following equations :
$\sqrt{3 x + 1}$ $-$ $\sqrt{x - 1}$ = $2$

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Solution

$⟹ \sqrt{3 x + 1} - \sqrt{x - 1} = 2 ⟹ \sqrt{3 x + 1} = 2 + \sqrt{x - 1} ⟹ {(\sqrt{3 x + 1})}^{2} = {(2 + \sqrt{x - 1})}^{2} ⟹ 3 x + 1 = 4 + {(\sqrt{x - 1})}^{2} + 2 (2) (\sqrt{x - 1}) ⟹ 3 x + 1 = 4 + x - 1 + 4 \sqrt{x - 1} ⟹ 3 x + 1 - 4 - x + 1 = 4 \sqrt{x - 1} ⟹ 2 x - 2 = 4 \sqrt{x - 1} ⟹ {(2 x - 2)}^{2} = 4^{2} (x - 1) ⟹ 4 x^{2} + 4 - 8 x = 16 (x - 1) ⟹ 4 x^{2} + 4 - 8 x = 16 x - 16 ⟹ 4 x^{2} - 8 x - 16 x = - 4 - 16 ⟹ 4 x^{2} - 24 x = - 20 ⟹ 4 x^{2} - 24 x + 20 = 0 ⟹ x^{2} - 6 x + 5 = 0 ⟹ x^{2} - 5 x - x + 5 = 0 ⟹ x (x - 5) - 1 (x - 5) = 0 ⟹ (x - 5) (x - 1) = 0 ⟹ x = 1 o r x = 5$

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